Question 665403

What is the solution to this system of linear equations using the substitution method?
1/2x-1/5y=6
1/6+2/5y=9


{{{system ((1/2)x - (1/5)y = 6_______eq (i),
(1/6)x + (2/5)y = 9_______eq (ii))}}}

 
5x - 2y = 60 ----- Multiplying eq (i) by LCD, 10 ----- eq (iii)
5x + 12y = 270 ---- Multiplying eq (ii) by LCD, 30 ----- eq (iv)
- 14y = - 210 ------ Subtracting eq (iv) from eq (iii)


y = {{{(- 210)/- 14}}}, or {{{highlight_green(y = 15)}}}


5x - 2(15) = 60 ------ Substituting 15 for y in eq (iii)
5x - 30 = 60
5x = 90

x = {{{90/5}}}, or {{{highlight_green(x = 18)}}}


You should be able to do the check, in the original equations, i.e. eqs (i) & (ii)


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